A joint effort was undertaken on a Precision Segmented Reflector (PSR) Project. The missions in which the PSR is to be used will use large (up to 20 m in diameter) telescopes. The essential requirement for the telescopes is that the reflector surface of the primary mirror must be made extremely precise to allow no more than a few microns of errors and, additionally, this high surface precision must be maintained when the telescope is subjected to on-orbital mechanical and thermal disturbances. Based on the mass, size, and stability considerations, reflector surface formed by segmented, probably actively or passively controlled, composite panels are regarded as most suitable for future space based astronomical telescope applications. In addition to the design and fabrication of composite panels with a surface error of less than 3 microns RMS, PSR also develops related reflector structures, materials, control, and sensing technologies. As part of the planning effort for PSR Technology Demonstration, a system model which couples the reflector, consisting of panels, support truss and actuators, and the optical bench was assembled for dynamic simulations. Random vibration analyses using seismic data obtained from actual measurements at the test site designated for PSR Technology Demonstration are described.